   Theorem 2.1 [1]}
Let  \(H_{\,1},\, H_{\,2}\)  be two Hilbert spaces and \(U \,:\, H_{\,1} \,\rightarrow \, H_{\,2}\)  be a bounded linear operator with closed range \(\mathcal {R}_{\,U}\) .Then there exists a bounded linear operator  \(U^{\dagger } \,:\, H_{\,2} \,\rightarrow \, H_{\,1}\)   such that  \(U\,U^{\dagger }\,x \,=\, x\; \;\forall \; x \,\in \, \mathcal {R}_{\,U}\) .

